Patterns and the Tₙ rule
Finding the rule of a number pattern, and working out far terms with a position rule. Read one part at a time and tap “I know this”. Then test yourself in the quiz.
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Number patterns
- Find the rule: what happens from one term to the next? 3; 7; 11; 15 → +4.
- Patterns can also multiply or divide: 2; 6; 18; 54 → ×3.
- Some grow by a growing step: 1; 2; 4; 7; 11 → +1, +2, +3, +4.
- Patterns can cross 0: −5; −2; 1; 4; … → +3, the next term is 7. 10; 6; 2; −2; … → −4, the next term is −6. Counting down past 0 takes you into the negative numbers.
The position rule
To find a far term (e.g. the 50th), link the term to its position. Pattern 4; 7; 10; 13: term = 3 × position + 1. The 50th term = 3 × 50 + 1 = 151.
The step between terms becomes the number that multiplies the position. Then test the first term to find the extra number.
In Grade 7 we write the rule as Tₙ = 3n + 1, with n the position.
Remember this and test yourself
- Find the rule from term to term.
- Patterns can add, subtract, multiply or divide.
- Far terms: link the term to its position.
- The step becomes the number in front of the position.
Write these points in your book. Read them again the night before the test.
Step → multiply; first term → check.
Important words
First say the answer yourself, then turn the card over.
Match column A to column B
Tap a word in column A, then its meaning in column B. You can also start in column B.
True or false?
Read the question and the answer. Is the answer right? Tap True or False.
Now the real quiz!
The quiz has many more questions on this topic. Every question shows straight away whether you are right and explains why.
Take the quiz: Patterns and the Tₙ rule- Let your child work the examples on paper and explain them to you.
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Follows CAPS for Grade 7 Mathematics. Always check your teacher’s notes and textbook too.